Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
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a train is 460 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ? | "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 460 + 140 = 600 meter time = distance / speed = 600 * ( 2 / 25 ) = 48 seconds answer : d" | a ) 76 seconds , b ) 18 seconds , c ) 40 seconds , d ) 48 seconds , e ) 45 seconds | d | divide(add(460, 140), divide(multiply(45, const_1000), const_3600)) | add(n0,n2)|multiply(n1,const_1000)|divide(#1,const_3600)|divide(#0,#2)| | physics |
joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 6 of the remaining paint . how many gallons of paint has joe used ? | "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 6 ) * 270 = 45 gallons total paint used = 135 gallons . option b" | a ) 18 , b ) 135 , c ) 175 , d ) 216 , e ) 250 | b | add(multiply(divide(360, 4), 1), divide(subtract(360, multiply(divide(360, 4), 1)), 6)) | divide(n0,n2)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n4)|add(#3,#1)| | physics |
a train 100 m long crosses a platform 180 m long in 14 sec ; find the speed of the train ? | "d = 100 + 180 = 280 t = 14 s = 280 / 14 * 18 / 5 = 72 kmph answer : a" | a ) 72 kmph , b ) 58 kmph , c ) 54 kmph , d ) 94 kmph , e ) 59 kmph | a | subtract(multiply(14, multiply(180, const_0_2778)), 100) | multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)| | physics |
a meal cost $ 48.75 adn there was no tax . if the tip was more than 5 pc but less than 20 pc of the price , then the total amount paid should be : | "5 % ( 48.75 ) = 2.4375 20 % ( 48.75 ) = 9.75 total amount could have been 48.75 + 2.4375 and 48.75 + 9.75 = > could have been between 51.1875 and 58.5 = > approximately between 51 and 59 answer is c ." | a ) 60 - 65 , b ) 55 - 58 , c ) 51 - 59 , d ) 39 - 41 , e ) 38 - 40 | c | add(divide(multiply(48.75, 5), const_100), 48.75) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)| | general |
on a map , 1 inch represents 28 miles . how many c inches would be necessary to represent a distance of 383.6 miles ? | "c inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c" | a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7 | c | divide(383.6, 28) | divide(n2,n1)| | physics |
a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many apples f did each person get before 45 people joined the feast ? | "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons f = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c" | a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 . | c | add(divide(1430, add(divide(1430, add(add(const_10, const_10), const_2)), 45)), 9) | add(const_10,const_10)|add(#0,const_2)|divide(n0,#1)|add(n1,#2)|divide(n0,#3)|add(n2,#4)| | general |
if the wheel is 14 cm then the number of revolutions to cover a distance of 1232 cm is ? | "2 * 22 / 7 * 14 * x = 1232 = > x = 14 answer : c" | a ) a ) 15 , b ) b ) 10 , c ) c ) 14 , d ) d ) 12 , e ) e ) 11 | c | divide(1232, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 14)) | multiply(const_100,const_3)|multiply(const_1,const_10)|add(#0,#1)|add(#2,const_4)|divide(#3,const_100)|multiply(#4,const_2)|multiply(n0,#5)|divide(n1,#6)| | physics |
what is the volume of an tetrahedron with edge length of 1 ? | the answer is sqr ( 2 ) / 12 = 0.11785113 the following can be derived using the pythagorean theorem : the height of a face is 3.5 / 2 . the area of any face is 3.5 / 4 . the distance from any corner to the center of a joining face is 1 / 3.5 . the height of the tetrahedron is ( 2 / 3 ) . 5 the area is 1 / 3 * base * h... | ['a ) 3.11545466', 'b ) 0.76678113', 'c ) 0.11785113', 'd ) 2.11785113', 'e ) 0.11786667'] | c | divide(sqrt(const_2), add(const_10, const_2)) | add(const_10,const_2)|sqrt(const_2)|divide(#1,#0) | geometry |
an exam consists of 2 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 70 % is a passing grade , what is the probability that brian passes ? | "if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure ... | a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 219 / 256 , e ) 15 / 16 | a | add(divide(subtract(const_1, add(add(power(divide(const_1, const_2), 2), multiply(2, power(divide(const_1, const_2), 2))), multiply(multiply(2, const_3), power(divide(const_1, const_2), 2)))), const_10), subtract(const_1, add(add(power(divide(const_1, const_2), 2), multiply(2, power(divide(const_1, const_2), 2))), mult... | divide(const_1,const_2)|multiply(n0,const_3)|power(#0,n0)|multiply(n0,#2)|multiply(#1,#2)|add(#3,#2)|add(#5,#4)|subtract(const_1,#6)|divide(#7,const_10)|add(#8,#7)| | general |
the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 28 years . find the average age of the women ? | "20 + 28 + 8 * 2 = 64 / 2 = 32 answer : c" | a ) 87 , b ) 98 , c ) 32 , d ) 28 , e ) 37 | c | divide(add(add(20, 28), multiply(8, 2)), const_2) | add(n2,n3)|multiply(n0,n1)|add(#0,#1)|divide(#2,const_2)| | general |
a girl was riding her scooter . her father wanted to calculate her speed . he knew that the street was 600 meters from end to end . he saw his daughter make the roundtrip 6 times . it took her 20 minutes to complete those 6 trips . how fast was the girl riding her scooter in kilometers per hour ? | the distance of the street was 600 meters . the made the roundtrip 6 times , which would be 2 trips for each roundtrip . multiply 12 times 600 to get the total distance . 600 * 12 = 7200 meters of 7.2 km . the question asked for the speed in km / hour and 20 minutes is one third of an hour . multiply 7200 by 1 / 3 to g... | a ) 2 , b ) 2.4 , c ) 1.2 , d ) 2.1 , e ) 2.7 | b | divide(subtract(divide(divide(multiply(600, 6), const_1000), divide(20, const_60)), const_1), const_4) | divide(n2,const_60)|multiply(n0,n1)|divide(#1,const_1000)|divide(#2,#0)|subtract(#3,const_1)|divide(#4,const_4) | physics |
the ratio of two quantities is 2 : 3 . if each of the quantities is increased by 6 , what is the ratio of the new quantities ? | "let quantities are 2 x and 3 x ratio of quantities after each is increased by 6 = ( 2 x + 6 ) / ( 3 x + 6 ) for x = 1 , ( 2 x + 6 ) / ( 3 x + 6 ) = 8 / 9 for x = 2 , ( 2 x + 6 ) / ( 3 x + 6 ) = 10 / 12 the value of final expression is dependent on the value of x which ca n ' t be determined as per given information . ... | a ) 2 : 3 , b ) 6 : 7 , c ) 8 : 9 , d ) 8 : 3 , e ) it can not be determined from the information given | e | divide(add(2, 6), add(3, 6)) | add(n0,n2)|add(n1,n2)|divide(#0,#1)| | other |
a rower whose speed is 2.5 km / hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 0.5 km / hr . what is the rower ' s average speed ( in km / hr ) for the total journey ? | time upstream = d / 2 time downstream = d / 3 total time = d / 2 + d / 3 = 5 d / 6 average speed = 2 d / ( 5 d / 6 ) = 2.4 km / hr the answer is c . | a ) 2.2 , b ) 2.3 , c ) 2.4 , d ) 2.5 , e ) 2.6 | c | divide(add(subtract(2.5, 0.5), add(2.5, 0.5)), const_2) | add(n0,n1)|subtract(n0,n1)|add(#0,#1)|divide(#2,const_2) | general |
in what ratio should a variety of wheat costing rs . 3 per kg be mixed with another variety of wheat costing rs . 6.25 per kg to obtain a mixture costing rs . 4.50 per kg ? | let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 6.25 - 4.50 ) / ( 4.50 - 3 ) = 7 / 6 answer : b | a ) 8 : 6 , b ) 7 : 6 , c ) 5 : 6 , d ) 7 : 5 , e ) 6 : 7 | b | divide(add(6.25, divide(divide(4.5, 3), const_2)), add(4.5, divide(4.5, 3))) | divide(n2,n0)|add(n2,#0)|divide(#0,const_2)|add(n1,#2)|divide(#3,#1) | other |
in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 5,3 ) , ( 8,3 ) , ( 4,5 ) , ( 7,5 ) ? | "delta x will give us the dimension of one side of the parallelogram = 8 - 5 = 3 unit delta y will give us the dimension of the other side of parallelogram = 5 - 3 = 2 unit area of parallelogram = 3 * 2 = 6 answer is e" | a ) 21 . , b ) 28 . , c ) 35 . , d ) 49 . , e ) 6 . | e | add(const_3, const_2) | add(const_2,const_3)| | geometry |
the captain of a cricket team of 11 members is 27 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ? | let the average age of the whole team be x years . 11 x - ( 27 + 30 ) = 9 ( x - 1 ) 11 x - 9 x = 48 2 x = 48 x = 24 . the average age of the team is 24 years . the answer is d . | a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25 | d | divide(subtract(add(27, add(27, 3)), multiply(3, 3)), const_2) | add(n1,n2)|multiply(n2,n2)|add(n1,#0)|subtract(#2,#1)|divide(#3,const_2) | general |
angelina walked 180 meters from her home to the grocery at a constant speed . she then walked 240 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to t... | "let the speed be x . . . so time taken from home to grocery = 180 / x . . the speed to gym = 2 x . . so time taken = 240 / 2 x = 120 / x . . its given 180 / x - 120 / x = 40 . . 60 / x = 40 = > 40 x = 60 = > x = 60 / 40 x = 1.5 m / secs . . so grocery to gym = 2 * 1.5 = 3 m / s . . . answer : b" | a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12 | b | multiply(divide(subtract(180, divide(240, const_2)), 40), const_2) | divide(n1,const_2)|subtract(n0,#0)|divide(#1,n2)|multiply(#2,const_2)| | physics |
i have 150 pieces of cake . there are 50 friends in my house . i would like to give each friend the same amount of cake , how much should i give to each friend ? | 150 / 50 = 3 the answer is e . | a ) 12 , b ) 7 , c ) 9 , d ) 15 , e ) 3 | e | divide(150, 50) | divide(n0,n1) | general |
there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 4 days more ? | "760 - - - - 22 760 - - - - 20 x - - - - - 4 x * 4 = 760 * 20 x = 3800 760 - - - - - - - 3040 answer : b" | a ) 3022 , b ) 3040 , c ) 3099 , d ) 3088 , e ) 3066 | b | subtract(divide(multiply(760, subtract(22, const_2)), 4), 760) | subtract(n1,const_2)|multiply(n0,#0)|divide(#1,n2)|subtract(#2,n0)| | physics |
sandy buys an old scooter for $ 900 and spends $ 300 on its repairs . if sandy sells the scooter for $ 1260 , what is the gain percent ? | "selling price / total cost = 1260 / 1200 = 1.05 the gain percent is 5 % . the answer is b ." | a ) 3 % , b ) 5 % , c ) 7 % , d ) 9 % , e ) 11 % | b | multiply(divide(subtract(1260, add(300, 900)), add(300, 900)), const_100) | add(n0,n1)|subtract(n2,#0)|divide(#1,#0)|multiply(#2,const_100)| | gain |
find the amount on rs . 8000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ? | "8000 * 104 / 100 * 105 / 100 = > 8736 answer : c" | a ) 5568 , b ) 6369 , c ) 8736 , d ) 5635 , e ) 6734 | c | divide(multiply(divide(multiply(8000, add(const_100, 4)), const_100), add(const_100, 5)), const_100) | add(n3,const_100)|add(n2,const_100)|multiply(n0,#1)|divide(#2,const_100)|multiply(#0,#3)|divide(#4,const_100)| | gain |
of the 1000 inhabitants of a town , 60 % are males of whom 20 % are literate . if , of all the inhabitants , 25 % are literate , then what percent of the females of the town are literate ? | sol . number of males = 60 % of 1000 = 600 . number of females = ( 1000 - 600 ) = 400 . number of literates = 25 % of 1000 = 250 . number of literate males = 20 % of 600 = 120 . number of literate females = ( 250 - 120 ) = 130 . ∴ required percentage = ( 130 / 400 x 100 ) % = 32.5 % answer c | a ) 22.5 , b ) 27.5 , c ) 32.5 , d ) 37.5 , e ) none | c | multiply(divide(subtract(multiply(divide(25, const_100), 1000), multiply(divide(20, const_100), multiply(1000, divide(60, const_100)))), subtract(1000, multiply(1000, divide(60, const_100)))), const_100) | divide(n3,const_100)|divide(n2,const_100)|divide(n1,const_100)|multiply(n0,#0)|multiply(n0,#2)|multiply(#1,#4)|subtract(n0,#4)|subtract(#3,#5)|divide(#7,#6)|multiply(#8,const_100) | gain |
how much water must be added to 68 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ? | "c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 68 litres of milk = ( 1 ⁄ 4 × 68 ) litres = 17 litres . answer b" | a ) 10 litres , b ) 17 litres , c ) 15 litres , d ) 18 litres , e ) none of these | b | divide(20, add(1, divide(1, 2))) | divide(n1,n3)|add(n1,#0)|divide(n4,#1)| | general |
i bought two books ; for rs . 600 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ? | "x * ( 85 / 100 ) = ( 600 - x ) 119 / 100 x = 350 answer : e" | a ) 197 , b ) 280 , c ) 189 , d ) 278 , e ) 350 | e | divide(multiply(600, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19))) | add(n2,const_100)|subtract(const_100,n1)|add(#0,#1)|multiply(n0,#0)|divide(#3,#2)| | gain |
if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 , 8 } , what is the probability that xy will be even ? | "probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 1 / 2 . answer : c ." | a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6 | c | divide(power(2, 2), multiply(choose(4, 2), choose(2, 1))) | choose(n3,n1)|choose(n1,n0)|power(n1,n1)|multiply(#0,#1)|divide(#2,#3)| | probability |
the largest four digit number which is a multiple of 8 , 10,12 and 15 is : | "lcm = 120 9999 / 120 = 83 83 * 120 = 9960 answer : a" | a ) 9960 , b ) 9950 , c ) 9940 , d ) 9930 , e ) 9920 | a | square_area(const_pi) | square_area(const_pi)| | general |
in how many ways can the integer 84 be expressed as a product of two different positive integers ? | "84 = ( 2 ^ 2 ) * 3 * 7 since 84 is not a perfect square , no of ways = 4 answer d" | a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2 | d | subtract(divide(divide(84, const_1), const_3), const_3) | divide(n0,const_1)|divide(#0,const_3)|subtract(#1,const_3)| | general |
find the value of y from ( 12 ) ^ 3 x 6 ^ 2 ÷ 432 = y ? | "144 e" | a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 144 | e | divide(multiply(power(12, 3), power(6, 2)), 432) | power(n0,n1)|power(n2,n3)|multiply(#0,#1)|divide(#2,n4)| | general |
a man buys an article for $ 20 . and sells it for $ 35 . find the gain percent ? | "c . p . = $ 20 s . p . = $ 35 gain = $ 15 gain % = 15 / 20 * 100 = 75 % answer is d" | a ) 25 % , b ) 50 % , c ) 20 % , d ) 75 % , e ) 30 % | d | subtract(divide(35, divide(20, const_100)), const_100) | divide(n0,const_100)|divide(n1,#0)|subtract(#1,const_100)| | gain |
a ball dropped from h height and moves 80 % of height each time . total distance covered is | first time distance is h second time 80 h / 100 = 4 h / 5 similarly third time 80 % of 4 h / 5 = h ( 4 ^ 2 ) / ( 5 ^ 2 ) and so on . . . this will lead to infinite terms of geometric progression i . e h + 2 * 4 h / 5 + 2 * 16 h / 25 . . . . . . . . . . . . sum = h + 2 * 4 h / ( 5 ( 1 - 4 / 5 ) ) = 9 h answer : d | a ) 4 h , b ) 5 h , c ) 7 h , d ) 9 h , e ) 8 h | d | add(divide(80, const_10), const_1) | divide(n0,const_10)|add(#0,const_1) | gain |
calculate 73196 ÷ ? = 631 | "answer let 62976 / x = 631 then x = 62976 / 631 = 116 option : d" | a ) 101 , b ) 116 , c ) 119 , d ) 116 , e ) 32 | d | multiply(73196, 631) | multiply(n0,n1)| | general |
two trains of equal length , running with the speeds of 60 and 20 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ? | "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 20 = 80 * 5 / 18 t = 2500 / 9 * 18 / 400 = 12.5 sec . answer : a" | a ) 12.5 , b ) 8.01 , c ) 7.5 , d ) 26 , e ) 22 | a | multiply(multiply(multiply(const_0_2778, subtract(60, 20)), 50), inverse(multiply(const_0_2778, add(60, 20)))) | add(n0,n1)|subtract(n0,n1)|multiply(#0,const_0_2778)|multiply(#1,const_0_2778)|inverse(#2)|multiply(n2,#3)|multiply(#4,#5)| | physics |
on the number line , the number p is twice as many units from - 2 as - 2 is from 7 . if p is less than – 2 , what is the value of p ? | "distance between - 2 and 7 = 9 since number p is twice as many units from - 2 as - 2 is from 7 , therefore p can be - 20 since , p is less than - 2 , the value of p = - 20 answer a" | a ) – 20 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14 | a | subtract(negate(2), multiply(2, subtract(2, negate(2)))) | negate(n2)|subtract(n0,#0)|multiply(#1,n0)|subtract(#0,#2)| | general |
find value for x from below equation ? x + 1 = 4 | "1 . subtract 1 from both sides : x + 1 - 1 = 4 - 1 2 . simplify both sides : x = 3 d" | a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2 | d | subtract(4, 1) | subtract(n1,n0)| | general |
find large number from below question the difference of two numbers is 1325 . on dividing the larger number by the smaller , we get 5 as quotient and the 5 as remainder | "let the smaller number be x . then larger number = ( x + 1325 ) . x + 1325 = 5 x + 5 4 x = 1320 x = 330 large number = 330 + 1320 = 1650 answer : a" | a ) 1650 , b ) 1324 , c ) 1245 , d ) 1300 , e ) 1635 | a | multiply(divide(subtract(1325, 5), subtract(5, const_1)), 5) | subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)| | general |
jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 4 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ? | "u / i = 4 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 20 : 10 : 2 i . e . u : b = 20 : 2 answer : option d" | a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2 | d | divide(multiply(4, 5), multiply(1, 2)) | multiply(n0,n2)|multiply(n1,n3)|divide(#0,#1)| | other |
if 11 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes | "n ( n - 1 ) / 2 = 11 * 10 / 2 = 55 answer : a" | a ) 55 , b ) 42 , c ) 43 , d ) 44 , e ) 45 | a | divide(factorial(11), multiply(factorial(subtract(11, const_2)), factorial(const_2))) | factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4)| | general |
0.0005215 / 0.000305 x 6.2 = ? | "explanation : ? = 0.0005215 / 0.000305 x 6.2 = 10.6 answer : option a" | a ) 10.6 , b ) 11.3 , c ) 12.7 , d ) 13.4 , e ) 14.5 | a | divide(0.0005215, 0.000305) | divide(n0,n1)| | general |
the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 25 % . by approximately what percent would the output now have to be decreased in order to restore the original output ? | "the original output increases by 10 % and then 25 % . total % change = a + b + ab / 100 total % change = 10 + 25 + 10 * 25 / 100 = 37.5 % now , you want to change it to 0 , so , 0 = 37.5 + x + 37.5 x / 100 x = - 37.5 ( 100 ) / 137.5 = 27 % approximately answer is d" | a ) 20 % , b ) 24 % , c ) 30 % , d ) 27 % , e ) 79 % | d | divide(multiply(subtract(add(add(const_100, 10), multiply(add(const_100, 10), divide(25, const_100))), const_100), const_100), add(add(const_100, 10), multiply(add(const_100, 10), divide(25, const_100)))) | add(n0,const_100)|divide(n1,const_100)|multiply(#0,#1)|add(#0,#2)|subtract(#3,const_100)|multiply(#4,const_100)|divide(#5,#3)| | general |
a and b started a business investing rs . 24,000 and rs 18,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ? | "a : b = 24000 : 18000 = 8 : 6 = 4 : 3 answer : a" | a ) 4 : 3 , b ) 9 : 2 , c ) 18 : 20 , d ) 1 : 4 , e ) 18 : 4 | a | divide(add(multiply(multiply(const_3, const_3), add(multiply(const_3, const_3), const_1)), 2), multiply(2, add(multiply(const_3, const_3), const_1))) | multiply(const_3,const_3)|add(#0,const_1)|multiply(#1,#0)|multiply(n2,#1)|add(n2,#2)|divide(#4,#3)| | gain |
find 283 / 1983 × 100 | "never start finding common factors . adjust the denominator to 2000 . so we are introducing an error of 17 which is 171983 = 1117171983 = 1117 th of the denominator . 283002000 = 14.15283002000 = 14.15 but this answer is slightly less than actual answer . now 14 . 1511714.15117 = 0.12 approximately . adding 0.12 to 14... | a ) 14.29 , b ) 14.21 , c ) 14.22 , d ) 14.27 , e ) 14.23 | b | divide(283, 1983) | divide(n0,n1)| | general |
three unbiased coins are tossed . what is the probability of getting at least 2 tails ? | "explanation : s = { hhh , hht , hth , htt , thh , tht , tth , ttt } e = { htt , tht , tth , ttt } n ( s ) = 8 n ( e ) = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 8 = 0.5 answer is b" | a ) 0.75 , b ) 0.5 , c ) 0.25 , d ) 0.2 , e ) 0.3 | b | negate_prob(divide(const_1, power(const_2, const_3))) | power(const_2,const_3)|divide(const_1,#0)|negate_prob(#1)| | probability |
compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 342 grams of compound x ? | "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 342 gms of x have 342 * 10 / 12 = 280 gms of b and 342 - 280 = 62 gms of a . cross check : - a / b = 62 / 280 = 2 / 10 ( as given ) ans e" | a ) 54 , b ) 162 , c ) 250 , d ) 270 , e ) 280 | e | divide(multiply(342, 10), add(2, 10)) | add(n0,n1)|multiply(n1,n2)|divide(#1,#0)| | other |
a certain article of clothing was discounted during a special sale to 4 / 5 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale... | "say the original retail price of the item was $ 200 . the price after the first sale = 4 / 5 * $ 200 = $ 160 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 160 - 100 ) / 150 = 1 / 3 = 40 % . answer : c ." | a ) 50 % , b ) 33.33 % , c ) 40 % , d ) 16.66 % , e ) 12.5 % | c | multiply(subtract(divide(4, 5), multiply(divide(4, 5), divide(1, 2))), const_100) | divide(n0,n1)|divide(n2,n3)|multiply(#0,#1)|subtract(#0,#2)|multiply(#3,const_100)| | gain |
income and expenditure of a person are in the ratio 8 : 7 . if the income of the person is rs . 40000 , then find his savings ? | "let the income and the expenditure of the person be rs . 8 x and rs . 7 x respectively . income , 8 x = 40000 = > x = 5000 savings = income - expenditure = 8 x - 7 x = x so , savings = rs . 5000 . answer : a" | a ) 5000 , b ) 6000 , c ) 7000 , d ) 8000 , e ) 9000 | a | subtract(40000, multiply(divide(7, 8), 40000)) | divide(n1,n0)|multiply(n2,#0)|subtract(n2,#1)| | other |
workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.50 lacs . how many workers were they ? | "n * 50 = ( 350000 - 300000 ) = 50000 n = 50000 / 50 = 1000 e" | a ) 220 , b ) 230 , c ) 500 , d ) 560 , e ) 1000 | e | divide(multiply(multiply(subtract(3.50, 3), const_1000), const_100), 50) | subtract(n2,n0)|multiply(#0,const_1000)|multiply(#1,const_100)|divide(#2,n1)| | general |
how many positive integers less than 60 have a reminder 01 when divided by 4 ? | "1 also gives the remainder of 1 when divided by 4 . so , there are total of 15 numbers . answer : c ." | a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17 | c | divide(factorial(subtract(add(const_4, 01), const_1)), multiply(factorial(01), factorial(subtract(const_4, const_1)))) | add(n1,const_4)|factorial(n1)|subtract(const_4,const_1)|factorial(#2)|subtract(#0,const_1)|factorial(#4)|multiply(#1,#3)|divide(#5,#6)| | general |
a boat goes 100 km downstream in 10 hours , and 200 km upstream in 25 hours . the speed of the stream is ? | "100 - - - 10 ds = 10 ? - - - - 1 200 - - - - 30 us = 8 ? - - - - - 1 s = ( 10 - 8 ) / 2 = 1 kmph . answer : a" | a ) 1 , b ) 22 1 / 7 , c ) 2 , d ) 22 1 / 2 , e ) 3 | a | divide(subtract(divide(100, 10), divide(200, 25)), const_2) | divide(n0,n1)|divide(n2,n3)|subtract(#0,#1)|divide(#2,const_2)| | physics |
if 25 % of x is 30 less than 20 % of 1000 , then x is ? | "25 % of x = x / 4 ; 20 % of 1000 = 20 / 100 * 1000 = 200 given that , x / 4 = 200 - 30 = > x / 4 = 170 = > x = 680 . answer : d" | a ) 188 , b ) 216 , c ) 156 , d ) 680 , e ) 121 | d | divide(subtract(multiply(1000, divide(20, const_100)), 30), divide(25, const_100)) | divide(n2,const_100)|divide(n0,const_100)|multiply(n3,#0)|subtract(#2,n1)|divide(#3,#1)| | general |
mr . bhaskar is on tour and he has rs . 360 for his expenses . if he exceeds his tour by 4 days , he must cut down his daily expenses by rs . 3 . for how many days is mr . bhaskar on tour ? | if his tour is for x days and he is spending rs y per day , then xy = 360 x = 360 / y or y = 360 / x ( x + 4 ) * ( y - 3 ) = 360 or xy + 4 y - 3 x - 12 = 360 or 4 y - 3 x - 12 = 0 4 * 360 / x - 3 x - 12 = 0 solving it , we get x = 20 answer : b | a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50 | b | divide(360, multiply(multiply(const_3, const_3), const_2)) | multiply(const_3,const_3)|multiply(#0,const_2)|divide(n0,#1) | physics |
a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability z that out of the two , one is white and one is blue ? | "the required probability z = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( ... | a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14 | d | divide(multiply(3, 5), divide(multiply(add(3, 5), add(5, const_2)), const_2)) | add(n0,n1)|add(n1,const_2)|multiply(n0,n1)|multiply(#0,#1)|divide(#3,const_2)|divide(#2,#4)| | probability |
a boat having a length 5 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of man is | "solution volume of water displaced = ( 5 x 3 x 0.01 ) m 3 = 0.15 m 3 . mass of man = volume of water displaced × density of water = ( 0.15 × 1000 ) kg = 150 kg . answer e" | a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none | e | multiply(multiply(multiply(5, 3), divide(1, const_100)), const_1000) | divide(n2,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(#2,const_1000)| | physics |
a batsman in his 15 th inning makes a score of 75 and their by increasing his average by 3 . what is his average after the 15 th inning ? | "14 x + 75 = 15 ( x + 3 ) x = 30 + 3 = 33 answer : c" | a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35 | c | add(subtract(75, multiply(3, 15)), 3) | multiply(n0,n2)|subtract(n1,#0)|add(n2,#1)| | general |
a man purchased 3 blankets @ rs . 100 each , 1 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ? | "10 * 150 = 1500 3 * 100 + 1 * 150 = 450 1500 – 450 = 1050 answer : a" | a ) 1050 , b ) 2770 , c ) 1550 , d ) 5102 , e ) 5000 | a | subtract(multiply(const_10, 150), add(multiply(3, 100), multiply(1, 150))) | multiply(n3,const_10)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|subtract(#0,#3)| | general |
five bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8,10 seconds respectively . in 60 minutes , how many times do they toll together ? | l . c . m of 2 , 4,6 , 8,10 is 240 . i . e after each 2 min they will toll together . so in 60 min they will toll 30 times . as they have initially tolled once , the answer will be 30 + 1 = 31 . answer : c | a ) 41 , b ) 10 , c ) 31 , d ) 16 , e ) 17 | c | divide(60, divide(multiply(multiply(2, multiply(multiply(add(const_2, const_3), 2), const_3)), 2), const_60)) | add(const_2,const_3)|multiply(n0,#0)|multiply(#1,const_3)|multiply(n0,#2)|multiply(n0,#3)|divide(#4,const_60)|divide(n4,#5) | physics |
a cube of side 4 meter length is cut into small cubes of side 25 cm each . how many such small cubes can be obtained ? | "along one edge , the number of small cubes that can be cut = 400 / 25 = 16 along each edge 16 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 16 * 16 * 16 = 4096 answer : d" | a ) 4069 , b ) 6048 , c ) 1000 , d ) 4096 , e ) 4060 | d | divide(power(power(4, const_2), const_3), power(4, const_3)) | power(n0,const_2)|power(n0,const_3)|power(#0,const_3)|divide(#2,#1)| | physics |
on a certain date , pat invested $ 6,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24,000 , in how many years total will the total value of the investment plus interest increase to $ 48,000 ? | "24,000 = 6,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 48,000 = 6000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ." | a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24 | a | divide(log(divide(multiply(const_3, const_10), add(const_4, const_1))), log(power(divide(multiply(const_2, const_10), add(const_4, const_1)), divide(const_1, 10)))) | add(const_1,const_4)|divide(const_1,n1)|multiply(const_10,const_3)|multiply(const_10,const_2)|divide(#2,#0)|divide(#3,#0)|log(#4)|power(#5,#1)|log(#7)|divide(#6,#8)| | general |
if | y + 7 | = 12 , what is the sum of all the possible values of y ? | there will be two cases y + 7 = 12 or y + 7 = - 12 = > y = 5 or y = - 19 sum of both the values will be - 19 + 5 = - 14 answer : a | a ) - 14 , b ) - 12 , c ) - 8 , d ) 8 , e ) 12 | a | add(subtract(12, 7), subtract(negate(12), 7)) | negate(n1)|subtract(n1,n0)|subtract(#0,n0)|add(#1,#2) | general |
the tax on a commodity is diminished by 15 % and its consumption increased by 10 % . the effect on revenue is ? | "100 * 100 = 10000 85 * 110 = 9350 - - - - - - - - - - - 10000 - - - - - - - - - - - 650 100 - - - - - - - - - - - ? = > 6.5 % decrease answer : b" | a ) 8.5 , b ) 6.5 , c ) 5.5 , d ) 5.6 , e ) 4.4 | b | subtract(const_100, multiply(multiply(add(const_1, divide(10, const_100)), subtract(const_1, divide(15, const_100))), const_100)) | divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)|subtract(const_100,#5)| | general |
positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 25 . what is the value of x ? | "y = 0.5 * 0.5 * x = x / 4 y % * x = 25 ( y / 100 ) * x = 25 ( x / 400 ) * x = 25 x ^ 2 = 25 * 400 x = 100 the answer is d ." | a ) 25 , b ) 50 , c ) 75 , d ) 100 , e ) 125 | d | multiply(multiply(divide(50, 25), divide(50, 25)), const_1000) | divide(n0,n2)|divide(n1,n2)|multiply(#0,#1)|multiply(#2,const_1000)| | general |
cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 78.2 after it went on sale for 15 % off , what is the difference between the original price and... | "0.85 * { original price } = $ 78.2 - - > { original price } = $ 92 . { final price } = $ 78.2 * 1.25 = $ 97.75 . the difference = $ 97.75 - $ 92 = $ 5.75 answer : b ." | a ) $ 0.00 , b ) $ 5.75 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.80 | b | subtract(multiply(78.2, divide(add(const_100, 25), const_100)), divide(78.2, divide(subtract(const_100, 15), const_100))) | add(n1,const_100)|subtract(const_100,n0)|divide(#0,const_100)|divide(#1,const_100)|divide(n2,#3)|multiply(n2,#2)|subtract(#5,#4)| | general |
evaluate 20 % of 450 + 45 % of 200 | "explanation : = ( 20 / 100 ) * 450 + ( 45 / 100 ) * 200 = 180 option e" | a ) 232 , b ) 242 , c ) 252 , d ) 262 , e ) 180 | e | divide(20, divide(450, 20)) | divide(n1,n0)|divide(n0,#0)| | gain |
which greatest possible length can be used to measure exactly 12 meter 34 cm , 8 meter 98 cm and 6 meter 65 cm | explanation : convert first all terms into cm . i . e . 1234 cm , 898 cm , 665 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 1 . option a | a ) 1 cm , b ) 2 cm , c ) 24 cm , d ) 55 cm , e ) 50 cm | a | floor(divide(add(multiply(12, const_100), 34), add(multiply(8, const_100), 98))) | multiply(n0,const_100)|multiply(n2,const_100)|add(n1,#0)|add(n3,#1)|divide(#2,#3)|floor(#4) | physics |
working together , printer a and printer b would finish the task in 20 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 4 pages a minute more than printer a ? | "20 * a + 20 * b = x pages in 20 mins printer a will print = 20 / 60 * x pages = 1 / 3 * x pages thus in 20 mins printer printer b will print x - 1 / 3 * x = 2 / 3 * x pages also it is given that printer b prints 4 more pages per min that printer a . in 20 mins printer b will print 80 more pages than printer a thus 2 /... | a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 340 | c | multiply(divide(4, subtract(divide(60, 20), const_1)), 60) | divide(n1,n0)|subtract(#0,const_1)|divide(n2,#1)|multiply(#2,n1)| | physics |
a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 20,000 and at the same time n is a perfect square and a perfect cube ? | "if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 . the answer is c ." | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | c | divide(add(const_4, const_2), const_1) | add(const_2,const_4)|divide(#0,const_1)| | geometry |
if 20 liters of chemical x are added to 80 liters of a mixture that is 30 % chemical x and 70 % chemical y , then what percentage of the resulting mixture is chemical x ? | "the amount of chemical x in the solution is 20 + 0.3 ( 80 ) = 44 liters . 44 liters / 100 liters = 44 % the answer is e ." | a ) 32 % , b ) 35 % , c ) 38 % , d ) 41 % , e ) 44 % | e | add(20, multiply(divide(30, const_100), 80)) | divide(n2,const_100)|multiply(n1,#0)|add(n0,#1)| | general |
the present population of a town is 60000 . the population increases annually at 10 % . find the population after 3 years . | explanation : solution : the required population is 60000 ( 1 + 10 / 100 ) ^ 3 = 60000 * 110 / 100 * 110 / 100 * 110 / 100 = 79860 answer : b | a ) 86000 , b ) 79860 , c ) 76300 , d ) 82900 , e ) none of these | b | divide(multiply(add(10, const_100), divide(multiply(add(10, const_100), divide(multiply(60000, add(10, const_100)), const_100)), const_100)), const_100) | add(n1,const_100)|multiply(n0,#0)|divide(#1,const_100)|multiply(#0,#2)|divide(#3,const_100)|multiply(#0,#4)|divide(#5,const_100) | gain |
sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 4 more than 1 / 4 of the fine and peter paid $ 4 less than 1 / 3 of the fine , leaving pay $ 5 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ? | "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 4 ] + [ ( 1 / 3 ) f – 4 ] + [ ( 1 / 2 ) f – 5 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 5 multiply all terms by 12 to clear the fract... | a ) $ 30 , b ) $ 25 , c ) $ 35 , d ) $ 40 , e ) $ 45 | b | add(multiply(add(multiply(add(divide(1, 2), add(divide(1, 4), divide(1, 3))), 5), 5), 2), const_10) | divide(n1,n2)|divide(n1,n5)|divide(n1,n8)|add(#0,#1)|add(#3,#2)|multiply(n6,#4)|add(n6,#5)|multiply(n8,#6)|add(#7,const_10)| | general |
the total car population in a chennai is 900 out of which 500 are made by honda . out of every 100 honda cars , 90 are red in color , but only 60 % of the total car population is red . find the % of non - honda cars that are red | "total honda brand red cars = 90 / 100 * 500 = 450 total red cars = 60 / 100 * 900 = 540 no . of non - honda cars = 900 - 500 = 400 no . of non - honda red cars = 540 - 450 = 90 % of non - honda red cars = 90 / 400 * 100 = 22.5 % answer : b" | a ) 20.5 % , b ) 22.5 % , c ) 21.5 % , d ) 10.5 % , e ) 32.5 % | b | subtract(add(const_12, const_12), divide(subtract(add(multiply(90, const_1), const_3), multiply(90, const_1)), const_2)) | add(const_12,const_12)|multiply(n3,const_1)|add(#1,const_3)|subtract(#2,#1)|divide(#3,const_2)|subtract(#0,#4)| | general |
find the least number of 5 digits which is exactly divisible by 12 , 15 and 18 ? | lcm = 180 180 ) 10000 ( 55 9900 - - - - - - - - - 100 10000 + 180 - 100 = 10080 answer : b | a ) 1080 , b ) 10080 , c ) 10025 , d ) 11080 , e ) 12080 | b | multiply(add(multiply(const_4, const_2), multiply(const_12, const_4)), lcm(lcm(12, 15), 18)) | lcm(n1,n2)|multiply(const_2,const_4)|multiply(const_12,const_4)|add(#1,#2)|lcm(n3,#0)|multiply(#3,#4) | general |
the length of a rectangle is 3 times its width . if the width of the rectangle is 5 inches , what is the rectangle ' s area , in square inches ? | "if the width is 5 in and the length is 3 times the width , then the length is 3 * 5 = 15 in the area is given by 5 * 15 = 75 square inches correct answer b" | a ) 30 square inches , b ) 75 square inches , c ) 68 square inches , d ) 89 square inches , e ) 92 square inches | b | rectangle_area(5, multiply(3, 5)) | multiply(n0,n1)|rectangle_area(n1,#0)| | geometry |
a certain sum amount to $ 1400 in 2 yrs and $ 2000 in 5 years on certain fixed simple interest . in how many yrs would the amount be $ 1640 had it been put at the rate of interest compounded annually ? | we can form equations as following : initial amount = p , total amount after interest = t , interest per year = i t = p + i given t 1 = p + 2 i = 1400 t 2 = p + 5 i = 2000 from this we get , p = 1000 i = 200 $ now we know that simple interest is < compound interest ( ci = si only after 1 st year if ci is compounded ann... | a ) 4.5 , b ) 3.5 , c ) 3 , d ) 2 , e ) 1.5 | e | add(divide(subtract(1640, 1400), divide(subtract(2000, 1400), subtract(5, 2))), subtract(divide(2, 5), divide(const_1, const_10))) | divide(n1,n3)|divide(const_1,const_10)|subtract(n4,n0)|subtract(n2,n0)|subtract(n3,n1)|divide(#3,#4)|subtract(#0,#1)|divide(#2,#5)|add(#7,#6) | gain |
the h . c . f . of two numbers is 15 and their l . c . m . is 620 . if one of the numbers is 375 , then the other is : | "other number = ( 15 x 620 ) / 375 = 24.8 . answer : e" | a ) 36.6 , b ) 42.8 , c ) 28.4 , d ) 11.6 , e ) 24.8 | e | multiply(15, 375) | multiply(n0,n2)| | physics |
from a pack of 52 cards , 1 card is drawn at random . find the probability of a face card drawn . | "explanation : total number of cases = 52 total face cards = 16 [ favourable cases ] so probability = 16 / 52 = 4 / 13 option a" | a ) 4 / 13 , b ) 1 / 52 , c ) 1 / 4 , d ) 1 / 3 , e ) none of these | a | divide(multiply(const_4, const_3), 52) | multiply(const_3,const_4)|divide(#0,n0)| | probability |
what is 92 % of 3 / 5 ? | "92 % * ( 3 / 5 ) = 0.92 * 0.6 = 0.552 answer : a" | a ) 0.552 , b ) 69.0 , c ) 0.6845 , d ) 0.6859 , e ) 0.69 | a | divide(multiply(92, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100) | add(const_2,const_3)|add(const_3,const_4)|add(const_3,const_3)|multiply(const_3,const_4)|multiply(#0,const_2)|multiply(#3,const_100)|multiply(#1,#0)|multiply(#4,#5)|multiply(#6,#4)|add(#7,#8)|add(#9,#2)|multiply(n0,#10)|divide(#11,const_100)| | gain |
if 9 a - b = 10 b + 80 = - 12 b - 2 a , what is the value of 2 a + 22 b ? | "this implies 9 a - b = 10 b + 80 , 9 a - b = - 12 b - 2 a , 10 b + 80 = - 12 b - 2 a manipulating the second equation gives us 10 b + 80 = - 12 b - 2 a = = > 2 a + 22 b = - 80 answer is c" | a ) - 4 , b ) - 2 , c ) - 80 , d ) 2 , e ) 4 | c | multiply(negate(multiply(divide(80, 2), 2)), 2) | divide(n2,n4)|multiply(#0,n4)|negate(#1)|multiply(n5,#2)| | general |
a can do a work in 24 days and b can do it in 8 days . in how many days a and b can do the work ? | "explanation : a ' s 1 day ' s work = 1 / 24 b ' s 1 day ' s work = 1 / 8 they work together = 1 / 24 + 1 / 8 = 6 days answer : option c" | a ) 20 days , b ) 10 days , c ) 6 days , d ) 8 days , e ) 7 days | c | divide(const_1, subtract(divide(const_1, 8), divide(const_1, 24))) | divide(const_1,n1)|divide(const_1,n0)|subtract(#0,#1)|divide(const_1,#2)| | physics |
the difference between the ages of two persons is 10 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the elder person is : | "solution let their ages be x year and ( x + 10 ) years respectively . then , ( x + 10 ) - 15 = 2 ( x - 15 ) ⇔ x - 5 = 2 x - 30 ⇔ x = 25 . ∴ present age of the elder person = ( x + 10 ) = 35 years . answer b" | a ) 25 years , b ) 35 years , c ) 45 years , d ) 55 years , e ) 75 years | b | add(subtract(10, subtract(10, add(const_3, const_2))), multiply(subtract(10, add(const_3, const_2)), const_2)) | add(const_2,const_3)|subtract(n0,#0)|multiply(#1,const_2)|subtract(n0,#1)|add(#2,#3)| | general |
sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 65 marks . how many sums did sandy get correct ? | "let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 65 5 x = 125 x = 25 the answer is d ." | a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27 | d | divide(add(multiply(2, 30), 65), add(2, 3)) | add(n0,n1)|multiply(n1,n2)|add(n3,#1)|divide(#2,#0)| | general |
a person distributed 20 % of his income to his 3 children each . he deposited 25 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 40000 . find his total income ? | "3 children got = 3 * 20 % = 60 % wife got = 25 % orphan house = 5 % total = 60 + 25 + 5 = 90 % remaining = 100 - 90 = 10 % 10 % = 40000 100 % = 40000 * 100 / 10 = $ 400000 answer is d" | a ) a ) 452000 , b ) b ) 562000 , c ) c ) 800000 , d ) d ) 400000 , e ) e ) 652000 | d | multiply(divide(40000, subtract(const_100, add(add(multiply(20, 3), 25), 5))), const_100) | multiply(n0,n1)|add(n2,#0)|add(n3,#1)|subtract(const_100,#2)|divide(n4,#3)|multiply(#4,const_100)| | gain |
the average weight of 4 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ? | "total weight increases = 4 × 1.5 = 6 kg so the weight of new person = 65 + 6 = 71 kg answer a" | a ) 71 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these | a | add(65, multiply(4, 1.5)) | multiply(n0,n1)|add(n2,#0)| | general |
convert 0.38 in to a vulgar fraction ? | "answer 0.38 = 38 / 100 = 19 / 50 correct option : d" | a ) 18 / 50 , b ) 16 / 50 , c ) 17 / 50 , d ) 19 / 50 , e ) none | d | divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 0.38), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2))) | add(const_2,const_3)|multiply(#0,const_2)|multiply(#1,#1)|multiply(n0,#2)|divide(#3,#2)| | physics |
on selling 17 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is : | ( c . p . of 17 balls ) - ( s . p . of 17 balls ) = ( c . p . of 5 balls ) c . p . of 12 balls = s . p . of 17 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 12 = rs . 60 . answer : b | a ) rs . 20 , b ) rs . 60 . , c ) rs . 40 , d ) rs . 30 , e ) rs . 90 | b | divide(720, subtract(17, 5)) | subtract(n0,n2)|divide(n1,#0) | gain |
when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 5 times , what is the probability that it will land on either side all 5 times ? | "must be either 5 heads or 5 tails 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 + 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 1 / 32 + 1 / 32 = 1 / 16 answer : d" | a ) 1 / 5 , b ) 1 / 10 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 32 | d | divide(const_1, power(const_2, const_4.0)) | power(const_2,const_4.0)|divide(const_1,#0)| | probability |
the average of 10 numbers is 210 . the average of first 5 numbers is 40 and the average of last 4 numbers is 200 . what is the middle number ? | the total of ten numbers = 10 x 210 = 2100 the total of first 5 and last 4 numbers is = 5 x 40 + 4 x 200 = 1000 so , the middle number is ( 2100 - 1000 ) = 1100 e | a ) a ) 200 , b ) b ) 2000 , c ) c ) 800 , d ) d ) 2100 , e ) e ) 1100 | e | subtract(subtract(multiply(210, 10), multiply(5, 40)), multiply(4, 200)) | multiply(n0,n1)|multiply(n2,n3)|multiply(n4,n5)|subtract(#0,#1)|subtract(#3,#2) | general |
a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 10 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have s... | "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.9 = $ 14 - - > x = $ 15.55 . therefore if the farmer had paid full price fo... | a ) $ 36.55 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60 | a | add(multiply(35, divide(40, const_100)), 35) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | gain |
a rectangular swimming pool is 20 feet by 22 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 728 square feet . what is the width of the deck ? | let the width = w total area of the pool and deck = ( 2 w + 20 ) ( 2 w + 22 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 24 * 26 has unit digit 8 . . . . . . . . . . eliminate b ) 2.5 feet . . . . . . . . . 25 * 33 has unit digit 5 . . . . . . . . . . eliminate c ) 3 fe... | ['a ) 2', 'b ) 4', 'c ) 3', 'd ) 5', 'e ) 6'] | c | divide(subtract(sqrt(add(power(subtract(22, const_1), const_2), subtract(728, rectangle_area(20, 22)))), subtract(22, const_1)), const_2) | rectangle_area(n0,n1)|subtract(n1,const_1)|power(#1,const_2)|subtract(n2,#0)|add(#2,#3)|sqrt(#4)|subtract(#5,#1)|divide(#6,const_2) | geometry |
three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 240 . their h . c . f is ? | "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 240 x = 4 the numbers are 3 * 4 , 4 * 4 , 5 * 4 hence required h . c . f . = 4 answer is c" | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | c | add(multiply(multiply(3, 5), const_100), multiply(4, 5)) | multiply(n0,n2)|multiply(n1,n2)|multiply(#0,const_100)|add(#2,#1)| | other |
a cistern is normally filled in 14 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ? | "1 / 14 - 1 / x = 1 / 16 x = 112 answer : e" | a ) 33 , b ) 88 , c ) 40 , d ) 99 , e ) 112 | e | inverse(subtract(divide(const_1, 14), divide(const_1, add(14, const_2)))) | add(n0,const_2)|divide(const_1,n0)|divide(const_1,#0)|subtract(#1,#2)|inverse(#3)| | physics |
the overall age of x and y is 15 year greater than the overall age of y and z . z is how many decades younger that x ? | b 15 ( x + y ) â € “ ( y + z ) = 15 x â € “ z = 15 | a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 19 | b | divide(15, const_1) | divide(n0,const_1) | general |
sachin is younger than rahul by 5 years . if the ratio of their ages is 7 : 9 , find the age of sachin | "if rahul age is x , then sachin age is x - 5 , so ( x - 5 ) / x = 7 / 9 = > 9 x - 45 = 7 x = > 2 x = 45 = > x = 22.5 so sachin age is 22.5 - 7 = 15.5 answer : e" | a ) 24.58 , b ) 24.5 , c ) 24.3 , d ) 24.9 , e ) 15.5 | e | multiply(divide(5, subtract(9, 7)), 7) | subtract(n2,n1)|divide(n0,#0)|multiply(n1,#1)| | other |
two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 42 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ? | "relative speed = 42 + 30 = 72 km / hr . 72 * 5 / 18 = 20 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 / 20 = 50 sec . answer : c" | a ) 22 , b ) 27 , c ) 50 , d ) 99 , e ) 12 | c | add(42, 30) | add(n1,n2)| | physics |
julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 128 and $ 140 from the simple interest account and the compound interest account respectively . if the interest rates for both account... | "$ 128 for 2 years = $ 64 per year . extra $ 12 yearned with the compound interest is the percent yearned on percent . so , $ 12 is yearned on $ 64 , which means that the interest = 5 % . this on the other hand means that half of the savings = 64 * 5 = $ 320 . twice of that = $ 640 . answer : a ." | a ) 640 , b ) 720 , c ) 1080 , d ) 1200 , e ) 1440 | a | divide(128, divide(multiply(const_2, subtract(140, 128)), 128)) | subtract(n1,n0)|multiply(#0,const_2)|divide(#1,n0)|divide(n0,#2)| | gain |
every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 2 / 5 of the juniors is equal to 1 / 3 of the seniors , what fraction of the students in the room are juniors ? | "let total number of juniors = j total number of seniors = s ( 2 / 5 ) j = ( 1 / 3 ) s = > s = 6 / 5 j total number of students = j + s = ( 11 / 5 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 11 / 5 ) j ] = 5 / 11 answer e" | a ) 3 / 20 , b ) 1 / 3 , c ) 5 / 12 , d ) 12 / 17 , e ) 5 / 11 | e | divide(multiply(5, 1), add(3, multiply(5, 5))) | multiply(const_2.0,const_2.0)|add(n3,#0)|divide(#0,#1)| | general |
dominos charges $ 6.25 for a veg pizza of std size that costs a total of $ 2.85 to make . pizza hut charges $ 5.80 for a similar pizza that costs $ 1.80 to make . if dominos sells 2000 pizzas , how many must pizza hut sell to make at least as much in total gross profit as its competitor does ? | dominos : profit / pizza = 6.25 - 2.85 = 3.75 : no of pizza = 2000 : gross profit = 2000 * 3.75 = 7500 pizza hut : profit / pizza = 4 : gross profit = 7500 : no of cups = 7500 / 4 = 1875 answer b | a ) 858 , b ) 1875 , c ) 14667 , d ) 63840 , e ) 146667 | b | add(divide(multiply(subtract(6.25, 2.85), 2000), subtract(5.8, 1.8)), const_100) | subtract(n0,n1)|subtract(n2,n3)|multiply(n4,#0)|divide(#2,#1)|add(#3,const_100) | general |
a certain company reported that the revenue on sales increased 20 % from 2000 to 2003 , and increased 40 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ? | "assume the revenue in 2000 to be 100 . then in 2003 it would be 120 and and in 2005 140 , so from 2003 to 2005 it increased by ( 140 - 120 ) / 120 = 20 / 120 = 17 % answer : e ." | a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 17 % | e | multiply(divide(subtract(add(const_1, divide(40, const_100)), add(const_1, divide(20, const_100))), add(const_1, divide(20, const_100))), const_100) | divide(n3,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|subtract(#2,#3)|divide(#4,#3)|multiply(#5,const_100)| | gain |
the average height of 30 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm . what was the actual average height of the students in the class ? | "the total height was 15 cm too much . the average height should be reduced by 15 cm / 30 = 0.5 cm the answer is a ." | a ) 174.5 , b ) 173.5 , c ) 172.5 , d ) 171.5 , e ) 170.5 | a | divide(subtract(multiply(30, 175), subtract(151, 136)), 30) | multiply(n0,n1)|subtract(n2,n3)|subtract(#0,#1)|divide(#2,n0)| | general |
how many integers are between 2 and 57 / 7 , inclusive ? | "57 / 7 = 8 . xx we are not concerned about the exact value of 57 / 7 as we just need the integers . the different integers between 2 and 57 / 7 would be 2,3 , 4 , 5 , 6 , 7 , 8 . total number of integers = 7 option b" | a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 12 | b | add(subtract(divide(57, 7), 2), const_1) | divide(n1,n2)|subtract(#0,n0)|add(#1,const_1)| | general |
mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 130 mangoes . | "mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total... | a ) 360 , b ) 380 , c ) 400 , d ) 406 , e ) 433 | e | multiply(divide(subtract(divide(360, subtract(const_1, divide(const_1, 10))), 360), 12), 130) | divide(const_1,n1)|subtract(const_1,#0)|divide(n0,#1)|subtract(#2,n0)|divide(#3,n2)|multiply(n3,#4)| | gain |
if 3 a – 2 b – 2 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 5 , what is the value of a + b + c ? | "when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets wor... | a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14 | b | subtract(subtract(add(subtract(subtract(subtract(subtract(subtract(subtract(subtract(32, 5), 5), 2), 2), const_1), 3), const_1), 2), 3), 5) | subtract(n3,n7)|subtract(#0,n7)|subtract(#1,n2)|subtract(#2,n2)|subtract(#3,const_1)|subtract(#4,n0)|subtract(#5,const_1)|add(n2,#6)|subtract(#7,n0)|subtract(#8,n7)| | general |
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